# E=mc² is Incomplete

E=mc^2 may be the most famous equation in the world… but what you might not know is
that it isn't the whole story. It just describes objects that have mass and that aren't moving.
The full equation is E, squared, equals m c squared, squared, plus p times c, squared,
where p represents the momentum of the object in question. This might all seem a bit confusing,
but in fact you can draw it as a right triangle with sides E, m c squared, and p times c - and
just use the pythagorean theorem (a squared plus b squared equals c squared) to give you
the equation.
Also, from here it's clear to see that for an object that isn't moving and thus doesn't
have any momentum and thus p is zero, we get back our good ole' friend E=mc2. On the other
hand, if the particle in question is massless (like light), then mass is zero and we get
E equals p times c. This tells us that the energy of a massless particle (like a photon
of light) is the same as its momentum (up to a factor of the speed of light).
In fact, the closer the energy of something is to p times c, the closer that something
is to behaving like light (I mean, look here, this tiny little bit of mass is hardly mass
at all).
Anyway, as an example, an object's velocity is equal to the speed of light times the ratio
of the object's momentum to energy - or pc over E. If your momentum increases, p times
c gets closer and closer to equaling your energy, so their ratio gets closer and closer
to being one, and your speed gets closer and closer to light speed. But because of that
tiny little bit of mass, the momentum side of the triangle will always be a little bit
smaller than the energy side. No matter how hard you try to increase your momentum, it
never quite gets to the point where p times c equals your energy, and thus your velocity
can never quite reach the speed of light, all because the hypotenuse of a right triangle
is longer than its legs.